Download - 2009 ESpring Prelim Sec 4Ex EM P1
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
1/23
J
Name : _____________________________________________________ ( )
Class : Sec 4/5____
Mathematics
Paper 1
Friday 21th
August 2009
Additional materials:nil
READ THESE INSTRUCTIONS FIRST
Write your Name and Index Number on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answerall questions.
If working is needed for any question, it must be shown with the answer.
Omission of essential working will result in loss of marks.You are expected to use an electronic calculator to evaluate explicit numerical
expressions. If the degree of accuracy is not specified in the question, and if the answer is
not, give the exact answer to three significant figures. Give answers in degrees to one
decimal place.
ForT, use either your calculator value or 3 142, unless the question requires the answer
in term ofT.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 80.
2 hour10:05 am 12:05 pm
This question paper consists of17 printed pages including the cover page.
4016/1
East Spring Secondary SchoolTowards Excellence and Success
Prelim Examination 2009Secondary 4 Express
MARKS:80
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
2/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 2/17
Mathematical Formulae
Compound interest
Total amount = 1100
nr
P
Mensuration
Curved surface area of a cone = rlT
Surface area of a sphere = 24 rT
Volume of a cone =
21
3 r hT
Volume of a sphere = 34
3rT
Area of triangle ABC=1
sin2
ab C
Arc length = rU , where U is in radians.
Sector area = 21
2
rU , where U is in radians.
Trigonometry
sin sin sin
a b c
A B C! !
2 2 2 2 cosa b c bc A!
Statistics
Mean =fx
f
Standard deviation =
22fx fx
f f
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
3/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 3/17
AnswerALL questions
1. Evaluate the following, expressing each answer in standard form.
(a) 0.5 2m in 2km (b) 325 m/s in km/h
Ans: (a) ___________ 2km [1]
(b) __________km/h [1]
2. A train leaves a station at 21 35and reaches its destination at 03 27.(a) Find the duration of the train journey in hour s and minutes.(b) Find the average speed of the train if it travels 322 km
Ans: (a)____h ______min [1]
(b) ___________km/h [1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
4/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 4/17
3. Solve
(a) 65
5.2 27!x
(b) 152 1 !x
Ans: (a) ______________ [1]
(b) ______________ [1]
4. Given thatA:B =3
1:
2
1and B:C= 3:1 .
Find the ratio ofA to Cin the formx:ywherexand yare integers.
Ans:A:C= ___________[2]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
5/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 5/17
5. Solve the following equations.
(a) 16)32( 2 !x
(b) 5)31(
1
)13(2
1!
yy
Ans: (a) ____________[2]
(b) ____________[2]
6. June wants to buy a type of chocolates from a DUTY FREE shop before shedeparts from Changi Airport for a school trip. The chocolates are sold at 55
cents a piece and packed into gift boxes that are sold at 80 cents each. Eachgift box can pack a maximum of 10 chocolates. If June has $35, find thenumber of pieces of the chocolates that she can buy at the most. .
Ans: _____________ [3]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
6/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 6/17
7. Express each of the following as a single matrix.
(a)
1
22
2
3
(b)
21
2323
Ans: (a) _______________ [1]
(b)_______________ [1]
8. A straight line, P,passes through the point (2, 10). The gradient ofP is 2.
(a)Write down the equation of the line P.
(b) Given that Palso passes through the point (k, k+3), find the value of k.
Ans: (a) ______________ [2]
(b) ______________ [1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
7/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 7/17
9. A = _ a17,13,11,10,8,6,3,1
B = _ a11,9,5,3,2
Given that set C is a subset ofA, n(C) = 7 and CB = _ a3 .
List the elements in set C
Ans: C = _____________ a [2]
10 Abby scores 65 marks and 79 marks for her first two tests. Find the lowestscore she needs to score in the third test if she wants to score an average of70 marks for the three tests.
Ans: ___________marks [2]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
8/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 8/17
11 Solve the following equation s simultaneously.0.3x+ 0.4y= 7
. 1.5x 0.3y= 8
Ans:x= ______, y= _______ [2]
12 The following data shows the number of 10 -cent coins in the wallets of eightstudents.
(a) The modal number of 10-cent coins is 11. Find the value ofx .
Hence, using this value ofx ,(b) Find the median of the data.(c) Find the mean of the data.
Ans: (a) ______________ [1]
(b) ______________ [1]
(c) ______________ [1]
11, 12, 10, 9, 8, ,1x 11, 12
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
9/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 9/17
13 The numbers below shows a sequence.
.
(a)Write down the 50 th term in the sequence.(b)Write down an expression, in terms of n, for the nth term of the
sequence
Ans: (a) ______________ [1]
(b) ______________ [1]
14 (a) Factorise completely
yxyx 15325 22
(b) Express as a single fraction.
2)62(2
33
y
yy
Ans: (a) ______________ [2 ]
(b) ______________ [2]
0, 3, 6, 9,
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
10/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 10/17
15 Given that yvaries inversely as 52 x and that2
120!x when
2
1!y , find
(a) yin terms ofx,
(b) the value ofxwhen 5!y .
Ans: (a) ______________ [2]
(b) ______________ [1]
16 The diagram shows the graph of ))(( xbxay ! .
From the graph,
find the value of a and b .
Ans: a = ______, b = _______ [2]
1 2
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
11/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 11/17
17 The diagram shows the speed - time graph of a cars journey. Calculate(a) the acceleration when t= 10,
(b) the speed when t= 10,
(c) the time taken by the car to travel 1.5 km.
Ans: (a) __________ 2/sm [1]
(b) ___________ sm / [1]
(c) ____________sec [2]
18 In the diagram, the straight line XYZ is parallel to PQ, and RY is parallel toQZ. r! 56XYR , r! 120QPR and r! 63YQZ . Calculate the value of
(a) YZQ (b) YQP
(c) YRP
Ans: (a) _____________0 [1]
(b) _____________0 [1]
(c) _____________0 [1]
240 40 60
Time
(tseconds)
60
Speed (metres per second)
Y
Z
P
Q
R
r56
r63 r120
X
S
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
12/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 12/17
19 The diagram below shows 3 cones that are geometrically similar. The heightof coneA and cone B are 18 cm and 6 cm respectively.
(a) If the base radius ofA is 6 cm, find the base radius of B.(b) If the base area ofA is 90 cm2, find the base area of B.
(c) The volume ofCis
64
1the volume ofA. Find the height of C.
Ans: (a) ____________cm [1]
(b) ____________cm2[2]
(c) ____________cm [2]
20 A polygon has n sides. Three of its exterior angles are rrr 15and28,67 while.
The remaining )3( n exterior angles are each equal to r50 . Find n.
Ans: n= ____________[2]
A B C
18
6
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
13/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 13/17
21 Using only ruler and compasses,(a) Draw and label clearly the triangle ABCwithAB = 7 cm,AC= 9 cm and
BC= 8 cm. [2](b) Measure and write down ABC .(c) Construct and label the angle bisector of ABC . [1](d) Construct and label the perpendicular bisector ofAC. [1]
.
Ans: (b) ____________o [1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
14/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 14/17
22 The school has tasked the DNT department to design souvenirs for thevisitors from oversea during the YOUTH OLYMIPIC GAMES (YOG) event.The souvenir consists of a trapezoidal prism with a cylindrical hole of radius10 cm in the centre.AB = 35 cm, EF= 85 cm, FG = 28 cm, CF= DE= 84 cmand the height of the solid is 80 cm.
Calculate the
(ai) total volume of the souvenir,
(ii) total surface area of the souvenir.
(b) If the souvenir is melted and recast into a cylindrical solid of height 80 cm,find the radius of the solid.
Ans: (a)(i)__________cm3 [2]
(ii) __________ cm2 [2]
(b) ___________cm [1]
G
F85 cm
28 cm
35 cm
80 cm10 cm
A
D
H
E
84 cm
B
C
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
15/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 15/17
23
In the diagram above A, B, C and D are points on level ground. D is duewest ofC, CD = 11 m, BC= 14 m,AC= 15 m and r! 112ACD . It is giventhat the bearing of CfromA is 202o and the bearing ofA from B is 318o.
Calculate(i) AD,(ii) the bearing ofA from C,(iii) AB
,(iv) shortest distance fromA to BC.
Ans: (i) ______________m[2]
(ii) ______________o[1]
(iii) _____________o [2]
(iv) ____________m [1]
11 m C
112o
15 m
14 m
N
A
B
D
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
16/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 16/17
24 The diagram shows a box-and-whisker plot for the following data set.
(a) Find the value of 3x .
(b) Find the interquartile range.(c) What does
15 xx mean for the data set?
Ans: (a) ____________ [1]
(b) ____________[1]
(c) ____________[1]
25 The position vectors relative to an origin O, ofA and B are
9
14
and3
2
respectively andAPB is a straight line.
(a) Find AB .
(b) Given further that ABAP4
3! find the position vector ofP.
Ans: (a) ______________ [1]
(b) ______________[2]
{12, 15, 18, 21, 22, 25, 29, 30, 31, 33, 38}
1x 2x 3x 4x 5x
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
17/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 17/17
26 Chen Han and Dan Dan play a game of chinese chess everyday. For each
game, the probability that Chen Han wins is8
3and the probability that Dan Dan
wins is5
2.
(a) Name the better player and explain why.(b) Calculate the probability that
(i) Chen Han wins on both Monday and Tuesday(ii) Dan Dan wins on eitherWednesday or Thursday but not on both
Wednesday and Thursday
Ans:
(a)____________________________________________________________ __ [1]
(b)(i) ____________[1]
(ii) ____________[2]
~End of Paper 1~
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
18/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 18/17
1a)
1b)
7105 v
31017.1 v
[B1]
[B1]
2a)
2b)
5 h 52 min
54.9 km/h [ecf]
[B1]
[B1]
3a)
3b)
3
1
[B1]
[B1]
4) A:B:C
1
1:
3
1:
2
1
A:C
2:11
1:
2
1
[M1]
[A1]
5a)
5b)
5.05.3
07124
169124
2
2
!
!
!
orx
xx
xx
3.0
930
)13(101
5)13(2
21
513
1
)13(2
1
!
!
!
!
!
y
y
y
y
yy
[M1]
[A1]
[M1]
[A1]
6)Cost of 10 chocolates with a box = 10(0.55) + 0.80 = $ 6.30
Maxiumum number of boxes: $35 30.6$z = 5.555 [ecf]
5} boxes
= 50 or 54 chocolates
[M1]
[M1]
[A1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
19/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 19/17
7a)
7b)
4
7
107
[B1]
[B1]
8a)
8b)
6
)2(210
!
!
!
c
c
cmxy
62 !@ xy
3
6)(23
!
!
k
kk [ecf]
[M1]
[A1]
[B1]
9) 1,3,6,8,10,13,17 [B2 for all
correct
answer]
[B1 for 1
error]
10)
66
3707965
!
v!
x
x
[M1]
[A1]
11) X= 7.68
Y= 11.7 [no ecf]
[B2 for all
correct
answer]
[B1 for 1
error]
12a)
12b)
12c)
12
11
10.5
[B1]
[B1]
[B1]
13a)
13b)
147
3n-3 or 3(n-1)
[B1]
[B1]
14a) yxyxyx 5355
355 yxyx
[M1]
[A1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
20/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 20/17
14b)2)3(4
2
3
3
y
y
y
2)3(2
718
)3)(3(4
1436
)3)(3(42
)3)(3(4)3)(4(3
)3)(3(4
2
3
3
!
!
!
!
y
y
yy
y
yyy
yyy
yy
y
y
[M1]
[A1]
15a)
15b)
35412
1
52
!
!
!
k
k
x
ky
52
3
!@
xy
3.4 [ecf]
[M1]
[A1]
[B1]
16) A= 1
B= 2
[B1]
[B1]
17a)
b)
c)
2.5
25 [ecf]
37
50242
1500)242(30
150060)24(2
1
!
!
!
!
t
t
t
tt
[B1]
[B1]
[M1]
[A1]
18a)
b)
c)
56
61 [ecf]
116
[B1]
[B1]
[B1]
19a)
19b)
2
10
18
6
90
2
!
!
x
x
[B1]
[M1]
[A1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
21/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 21/17
19c)
5.4
1864
13
!
!
x
x
[M1]
[A1]
20) 00000 360503152867 !v n
n=8
[M1]
[A1]
21a)
21b)
21c)
00 174 s
[A1] ---
Show construction line at ABC with accurate drawing
[A1] ---
Show construction line atAC with accurate drawing
[A2] ---
Show 2
construction
lines with
accuratedrawing
[A1] ---
Show 2
construction
lines with
accurate
drawing
[B1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
22/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
49229284.doc Towards Excellence and Success page 22/17
22a)
(i)
(ii)
b)
Vol of trap = 3400,134)28)(80(85352
1cm!
Total volume of souvenir =
)28()10)(142.3(400,134 2 =125,602.4cm3 [ecf]
Total surface area =
2
2
12.795,18
2820142.3
)10142.34800(2)2885()2835()8428(2
cm!
vv
vvvv
22.4 [ecf]
[M1]
[A1]
[M1]
[A1]
[B1]
23)
(i)
(ii)
(iii)
(iv)
Using cos rule,
AD =)112cos(151121511 022 vvv
= 21.7
000 02290112 !
000 644222 !!BA
Using Sine Rule,
0
0
4.74
15
sin
14
64
!
!
AB
AB
Sin
000 6.414.74.64180 !!A B [ecf]
96.9
156.41sin 0
!
!
x
x
[B2]
[B1]
[M1]
[A1]
[B1]
-
8/8/2019 2009 ESpring Prelim Sec 4Ex EM P1
23/23
East Spring Secondary SchoolMathematics DepartmentDo It Right. Always
24a)
24b)
24c)
25
13
range
[B1]
[B1]
[B1]
25a)
b)
12
12
!
!
9
9
12
12
4
3AP
!
!!
6
11
9
9
3
2APOAOP
[B1]
[M1]
[A1]
26a)
(bi)
(ii)
(iii)
Dan Dan. Her probability of winning is higher
64
9
8
3
8
3!v
25
12
5
2
5
3
5
3
5
2
!
vv
40
9
5
2
8
31 !
[B1]
[B1]
[M1]
[A1]
[B1]